The milky way rotation curve and its vertical derivatives: Inside the solar circle

We measure the Galactic rotation curve and its first two vertical derivatives in the first and fourth quadrants of the Milky Way using the 21 cm VGPS and SGPS. We find tangent velocities of the atomic gas as a function of Galactic longitude and latitude by fitting an analytic line profile to the edges of the velocity profiles. The shape of the analytic profile depends only on the tangent velocity and the velocity dispersion of the gas. We use two complementary methods to analyze the tangent velocities: a global model to fit typical parameter values and a local fitting routine to examine spatial variations. We confirm the validity of our fitting routines by testing simple models. Both the global and local fits are consistent with a vertical falloff in the rotation curve of -22 +/- 6 km s(-1) kpc(-1) within 100 pc of the Galactic midplane. The magnitude of the falloff is several times larger than what would be expected from the change in the potential alone, indicating some other physical process is important. The falloff we measure is consistent in magnitude with that measured in the halo gas of other galaxies.